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The objective function in our case consists of: i) maximising correlation between λ i and envirome variables (or equivalently between r(t) and x t)), and ii) minimising redundancy, i.e. eliminating all elementary modes with weak correlations with the envirome.
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The aim is to maximise correlation between the absolute flux and reaction data, but replacing v with | v| in the definition of Z would remove its convexity.
The model parameters were optimised, via an evolutionary algorithm, to maximise correlation between the fluorescent histograms generated numerically to that experimentally measured.
The cycle between FVA and maximising correlation is continued until no extra irreversible reactions are found through variability analysis.
An alternative objective function is presented, that is based upon maximising the correlation between experimentally measured absolute gene expression data and predicted internal reaction fluxes.
Instead, the focus is on maximising the correlation between the steady-state pattern of the predicted fluxes and the corresponding gene expression data at the biochemical level.
Instead, an iterative process is used to assign the data to the model: 1. Maximise the correlation between the initial set of irreversible reactions and the experimental data.
More recently, and in the context of GWAS, Yang et al. [ 75] used an approach similar to ours to find the P-value that maximise the correlation between the proportion of significant SNPs and the heritability across 47 traits.
The ICE algorithm uses the expectation/mean instead of the mode of the posterior, because (1) the mean of g maximises the correlation between g and g ^ [ 2]; and (2) due to the spike at zero the posterior may be bi-modal (see Results), in which case the mode may be quite far away from the mean.
The classes are then ordered in a two-dimensional output space by maximising the correlation coefficient (r) between the Euclidean distances separating the classes in data space and their corresponding distances in output space.
The MCA generates quantitative scores, called dimensions, which are linear combinations of the dummy variables that maximise the average correlation between them.6 The first dimension of the MCA that takes into account the largest part of the observed heterogeneity reflects the intensity in use of the selected tools.
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